The measurement and control of fluid flow can be said to be the very heart of the process industries. In particular, many processes in the semiconductor manufacturing industry require extreme accuracy and repeatability in gas delivery, and thus demand that the mass flow rate of process gases be precisely measured and controlled.
A typical thermal mass flow instrument measures gas flow by routing a small portion of the gas stream through a sensing tube. Heat is applied at the midpoint of the sensing tube, with temperature sensors located on either side of the heater. Each temperature sensor measures the temperature of the gas at its respective location. The first temperature sensor measures the gas temperature upstream of the heater. The second temperature sensor measures the gas temperature downstream of the heater and reflects a temperature corresponding to the gas as heated by the heater. The temperature difference of the gas on either side of the heater is proportional to the mass flow rate of the gas. The relationship between the temperature difference (".DELTA.T") and mass flow is affected by additional factors such as the specific heat of the gas. Taking these factors into consideration, the ideal relationship is expressed mathematically by the following equation: EQU .DELTA.T=A*P*C.sub.p *m
where .DELTA.T=temperature difference (.degree.K), A=constant of proportionality (s.sup.2 -K.sup.2 /kJ.sup.2), P=heater power, C.sub.p =specific heat of the gas at constant pressure and m=mass flow (kg/s). Additionally, other factors unique to each specific mass flow controller and its operating environment affect the above relationship, requiring that each instrument be calibrated to provide accurate mass flow information.
Ideally, manufacturers would calibrate individual mass flow instruments using the actual process gas to be measured in the user's process, based on user-provided operating requirements such as temperature and pressure conditions, flow rates, etc. To calibrate the instrument using a given process gas, the gas is put through the instrument under known conditions and flow rate and the meter is adjusted to provide the desired reading or output signal for the particular mass flow. This process would then be repeated for various flow rates across the instrument's measuring range, resulting in a series of actual output signals and their corresponding adjusted signals indicating mass flow.
The ideal calibration technique discussed above is not possible in practice because the gases to be measured and controlled in many industrial processes, and especially those used in semiconductor manufacturing, are often toxic, corrosive or environmentally unfriendly. For this reason, calibrating mass flow instruments with actual process gases in a production setting is often impractical or impossible. Instead, mass flow instruments are typically calibrated with a "safe" gas such as nitrogen, and a conversion constant is calculated based on properties of the process gas relative to properties of the safe gas. This conversion constant is then applied to the adjusted output signals across the measuring range of the instrument in an attempt to convert the calibration data obtained from the calibration with the safe gas to calibration data that is closer to that which would be expected from a calibration using the actual process gas.
For example, assume that a mass flow controller is calibrated with nitrogen. The gas actually flowing through the mass flow controller is carbon dioxide. Based on the ratio of the molar specific heat of the two gases, a conversion constant of 0.773 may be calculated for converting the flow signal from indicating the flow of nitrogen to the flow of carbon dioxide. If the mass flow controller calibrated with nitrogen has a flow signal indicating 75 standard cubic centimeters (sccm), the flow of carbon dioxide is computed by applying the conversion constant (0.773) to the output reading. Thus, if the mass flow controller reading is 75 sccm, the approximate carbon dioxide flow is 57.98 sccm (75*0.773). This conversion constant is typically applied linearly, or across the instrument's measuring range to convert the flow signal from indicating flow of the calibration gas to indicating flow of the desired process gas.
Applying a single conversion constant across a mass flow instrument's measuring range in this manner has generally proven unsatisfactory. Calculating the conversion constants requires accurate data regarding the process gas heat capacity (C.sub.p), but C.sub.p can be a strong and non-linear function of temperature and pressure, which results in a conversion constant that is accurate only for very limited conditions. In other words, the conversion constant necessary to accurately convert a signal indicating the mass flow of a calibration gas to a signal indicating the mass flow of a process gas will not be constant but may be significantly different for varying flow rates, temperatures, pressures, etc. This results significant errors in the final product produced by the process being measured and controlled.
In an attempt to compensate for this problem, prior art solutions, such as that disclosed in U.S. Pat. No. 5,062,446, apply a theoretical conversion factor (i.e., one based on relative gas properties) that is a function of mass flow rate rather than applying a single conversion constant across the measuring range of the mass flow instrument. In effect, this results in a different conversion factor for each flow rate.
As with applying a theoretical conversion constant across the mass flow instrument measuring range, applying a theoretical conversion factor as a function of flow rate generally is not a satisfactory solution to the problem of calibrating a mass flow controller with a gas other than the process gas. C.sub.p is not a well studied gas property for many of the semiconductor compounds, and reliable C.sub.p data do not exist for the nearly is 200 different gas compounds which mass flow instruments typically measure. Moreover, mass flow instruments are also affected by non-ideal factors which are a function of gas density and viscosity as well as the mass flow instrument's geometry, which can lead to inaccurate mass flow measurement with theoretical conversion factors whether applied linearly or as a function of flow rate.
An alternative to calibrating with a "safe" gas and using a theoretically calculated conversion factor is to calibrate the instrument with a "surrogate" gas. A surrogate gas is an inert gas that is selected to mimic as close as possible the thermal properties of the process gas, so it should result in better absolute accuracy when the process gas is measured with the instrument. Using a surrogate gas to calibrate thermal mass flow controllers also has not been adequate. Theoretically, the calibration data should be more accurate across the flow range, but this only holds true if the surrogate gas and the process gas have the same viscosity and density. Further, the thermal properties of the surrogate gas change with small changes in temperature and pressure, resulting in changes in calibration. This leads to instrument to instrument calibration differences, creating undesired variations in the users' processes. Moreover, if multiple process gases are to be measured and controlled with the same mass flow controller, some form of conversion is still necessary. Still further, freons comprise the most common surrogate gases, which are ozone depleting chemicals and do not fit in well with environmental responsibility.
Mass flow users have generally come to accept the above discussed shortcomings with calibrating mass flow meters and controllers as a fact of life. Users attempt to work around problems with mass flow meter and controller calibration by characterizing the mass flow instrument in the process by monitoring some characteristic of the final process, or using the pressure rise characteristics of the process vessel to measure the flow. These attempted solutions are also undesirable because they take time, waste production material, and are inaccurate and non-repeatable.